Iran's judiciary has opened an investigation into the death of a teenage girl, who was reportedly killed during protests over the death in police custody of 22-year-old Mahsa Amini.

A wave of unrest has rocked Iran since Amini died on September 16 after her arrest by the morality police in Tehran for allegedly failing to observe the Islamic republic's strict dress code for women.

The street violence has led to the deaths of dozens of people -- mostly protesters but also members of the security forces.

"A case has been filed in the criminal court to investigate the cause of Nika Shakrami's death," Tehran prosecutor Ali Salehi was quoted as saying by the official IRNA news agency late Tuesday.

"An order to investigate the case has been issued and necessary measures are being taken in this regard," he added.

Earlier, the prosecutor said 400 protesters were released from prison "on condition of not repeating their actions".

He stressed, however, that those "who acted against national security" will be dealt with "decisively, seriously and without leniency."